The reduction of porosity due to pressure solution is analyzed for some theoretical models consisting of aggregates of spherical grains of uniform size. The analysis is carried out for all six of the stable regular packing arrangements suggested by Graton and Fraser (1935). For each regular packing arrangement, two limiting cases are considered, one with all of the dissolved material removed from the system and the other with all of the material locally precipitated. Even for the most compact packing arrangement and complete local precipitation, the amount of vertical shortening for total porosity reduction is found to exceed 26 percent. A comparison of the amount of porosity reduction due to solution and the additional reduction due to precipitation of the dissolved material as cement indicates that for all cases, solution is more important in the early stages while cementation becomes more effective in the later stages. The exact relationship also varies according to the packing arrangement and its orientation with respect to the direction of compaction. Cases 1 and 6 show the maximum cementation-solution ratio while Case 3 shows the minimum ratio. The results obtained from studies of regular geometric arrays of spherical grains can be used to estimate the importance of pressure solution as compared to other porosity-reducing mechanisms in the diagenesis of well-sorted sandstones of uniform grain size. Any initial porosity in the sandstone can be represented by combinations of different volume proportions of the various packing arrangements. By comparing the "minus cement porosity" in a sandstone with the volume of cement predicted by a theoretical model, the role of pressure solution and the minimum volume of cement that has entered or left the system can be estimated.

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